There are two widely used time standards. One is the rotation of the
earth, and the other is the frequency of atomic oscillations (mainly the
cesium-133 atom). The earth's rotation is not uniform. Its rate exhibits
both periodic changes and long term drifts on the order of a second per
year. Atomic standards are the closest approximations we currently have
to a unform time with accuracies on the order of microseconds per year.

Since the advent of atomic time in 1955 there has been a steady transition
from reliance on the earth's rotation to the use of atomic time as the
primary standard. Before atomic time, the closest approximation to a
uniform time was Ephemeris Time (ET), which used the best available theory
of the earth's rotation to remove its known changes in rotation rate. The
use of Ephemeris Time continued until 1984. It was the time independent
variable for planetary ephemerides until then.

Several important time scales still follow the rotation of the earth, most
notably civil and sidereal time, but of these are now derived from atomic time
through a combination of earth rotation theory and actual measurements of
the earth's rotation and orientation. Chapter 2 of the most recent
Explanatory Supplement to the Astronomical Almanac [ref
1] gives an extensive summary of time standards and a list of original
literature references. The kinds of time typically encountered in astronomy
are briefly described below.

You will notice that many of the time acronyms are reversed from
their full English names. That's because they are acronyms from French (TAI
= Temps Atomique International) since France has a long and
continuing history as a primary source of time standards, now through the
Bureau International des Poids et Measures.

International Atomic Time (TAI) is the primary time standard in the world
today. It is the combined input of many clocks around the world, each
corrected for known environmental and relativistic effects. A few clocks,
such as the cesium clock ensemble at the U. S. Naval Observatory, carry
considerable weight in the TAI. In relativistic terms, TAI is an
earth-based time since it is defined for a gravitational potential and
inertial reference on the surface of the earth. TAI is the standard for
the SI (System International) second. The zero point of TAI was
somewhat arbitrarily defined by early atomic clocks, and it's offset from
Ephemeris Time was precisely defined as 32.184 seconds for January 1,
1977. See TDT below.

Coordinated Universal Time (UTC) is the time broadcast by WWV and other
services. By definition, UTC and TAI have the same rate, but UTC stays
close to Mean Solar Time by adding integer numbers of seconds, called leap
seconds, from time to time. This keeps solar noon at the same UTC
(averaged over the year), even though the rotation of the earth is slowing
down. The offset is changed as needed to keep UTC within about 0.7
seconds of earth rotation time, UT1. Leap seconds are
typically added once per year at the end of December or June, but they can
be added (or subtracted) at other designated times throughout the year. The
offset between TAI and UTC is currently 30 seconds, e.g., 20:00:00 UTC =
20:00:30 TAI.

UTC = TAI - (number of leap seconds)

Before UTC, the time broadcast by WWV and other services was a close
approximation to Greewich Mean Time (GMT) [ref 2].
GMT is an earth rotation time and is now called UT1 or simply UT.

Before atomic clocks, Ephemeris Time (ET) was the closest available
approximation to a uniform time for planetary motion calculations.
Terrestrial Dynamic Time, which is tied to atomic time by a constant
offset of 32.184 seconds, replaced ET at the beginning of 1984. The
purpose of the offset is to maintain continuity between ET and TDT at
the transition. Planetary motions are now computed using Barycentric Dynamic Time (TDB), which is more uniform
than TT because it accounts for relativistic corrections due to the
earth's motion in the gravitational potential of the solar system.

TT = TAI + 32.184 = UTC + (number of leap seconds) + 32.184

There is a subtle relativistic distinction between coordinate time and
dynamic time, which is not significant for most practical purposes. The
counterpart to TT is Geocentric Coordinate Time (TCG) which differs in
rate from TT by about 0.7 parts per billion [ref 3].
TT and TCG were coincident on January 1, 1977 and now differ by 0.42
seconds. The rate difference from TT can be important to long term
measurements, so make sure you know which time is being used when
comparing observations. Some physical constants are different in
coordinate time. You are not likely to encounter TCG in the literature.

Barycentric Dynamic Time (TDB) is the same as as Terrestrial Dynamic Time
(TT) except for relativistic corrections to move the origin to the solar
system barycenter. These corrections amount to as much as about 1.6
millisends and are periodic with an average of zero. The
dominant terms in this correction are have annual and semi-annual
periods.

and JD is the Julian Date. A more accurate formula, with adds terms
smaller than 20 microseconds, is given in the Explanatory Supplement to
the Astronomical Almanac [ref 4]. Planetary motions
are now computed using TDB.

There is a subtle relativistic distinction between coordinate time and
dynamic time, which is not significant for most practical purposes. The
counterpart to TDB is Barycentric Coordinate Time (TCB) which differs in
rate from TDB by about 15.5 parts per billion [ref 5].
TDB and TCB were coincident on January 1, 1977 and now differ by 9.3
seconds. The rate difference from TDB can be important to long term
measurements, so make sure you know which time is being used when
comparing observations. Some physical constants are different in
coordinate time. You are not likely to encounter TCB in the literature.

Universal Time (UT1) is a measure of the actual rotation of the earth,
independent of observing location. UT1 is essentially the same as the now
discontinued Greenwich Mean Time (GMT). It is the observed rotation of
the earth with respect to the mean sun corrected for the observer's
longitude with respect to the Greenwich Meridian and for the observer's
small shift in longitude due to polar motion.

Since the earth's rotation is not uniform, the rate of UT1 is not
constant, and its offset from atomic time is continually changing in a not
completely predictable way. As of December 1995, UT1 was drifting about
0.8 seconds per year with respect to atomic time (TAI or UTC). Since UTC
is intentionally incremented by integer seconds (leap seconds) to stay
within 0.7 seconds of UT1, the difference between UT1 and UTC is never
greater than this. The difference, DUT1 = UT1 - UTC is monitored by the
International Earth Rotation Service and published weekly in IERS Bulletin A along
with predictions for a number of months into the future.

UT1 = UTC + DUT1 (from the IERS Bulletin A)

Note that when a leap second is added to or subtracted from UTC, the value
of DUT1 is discontinuous by one second. UT1 is continuous, and UTC is
incremented or decremented by integer seconds to stay witin 0.7 seconds of
UT1.

UT0 (UT-zero) is an observatory-specific version of UT1 in the sense that
UT0 contains the effect of polar
motion on the observed rotation of the earth. Polar motion is
equivalent to a change in latitude and longitude of points on the earth's
surface with respect to the earth's instantaneous rotation axis. Since
UT1 is now determined from observations from an ensemble of obsevatories,
often as part of VLBI interferometers, the practical use of UT0 has
dwindled. The conversion from UT1 to a local observatory time with
respect to the mean sun or stars is now done as a set of coordinate
rotations that do not explicitly use UT0 as an intermediate step.

UT2 appears to be of mostly historical interest. Before 1972 the time
broadcast services kept their time signals within 0.1 seconds of UT2,
which is UT1 with annual and semiannual variations in the earth's
rotation removed. The formal relation between UT1 and UT2 is

Sidereal time is the measure of the earth's rotation with respect to
distant celestial objects. Compare this to UT1, which is the rotation of
the earth with respect to the mean position of the sun. One sidereal
second is approximately 365.25/366.25 of a UT1 second. In other words,
there is one more day in a sidereal year than in a solar year.

By convention, the reference points for Greenwich Sidereal Time
are the Greenwich Meridian and the vernal equinox (the intersection
of the planes of the earth's equator and the earth's orbit, the ecliptic).
The Greenwich sidereal day begins when the vernal equinox is on the
Greenwich Meridian. Greenwich Mean Sidereal Time (GMST) is the hour angle
of the average position of the vernal equinox, neglecting short term
motions of the equinox due to nutation.

In conformance with IAU conventions for the motion of the earth's equator
and equinox [ref 7] GMST is linked directly to UT1
through the equation

It might seem strange that UT1, a solar time, is
determined by measuring the earth's rotation with respect to distant
celestial objects, and GMST, a sidereal time, is derived from it. This
oddity is mainly due our choice of solar time in defining the atomic time
second. Hence, small variations of the earth's rotation are more easily
published as (UT1 - Atomic Time) differences. In practice, of course,
some form of sidereal time is involved in measuring UT1.

Greenwich Apparent Sidereal Time (GAST) is Greenwich Mean Sidereal Time
(GMST) corrected for the shift in the position of the
vernal equinox due to nutation. Nutation
is the mathematically predictable change in the direction of the earth's
axis of rotation due to changing external torques from the sun, moon and
planets. The smoothly varying part of the change in the earth's
orientation (precession) is already
accounted for in GMST. The right ascension component of nutation is
called the "equation of the equinoxes" [ref 9].

The definition of Local Sidereal Time given in the glossary of the
Explanatory Supplement to the Astronomical Almanac is "the local hour
angle of a catalog equinox." This fits the common text book definition

Hour Angle = LST - Right Ascension

where the right ascension can be specified in one of the catalog
coordinate systems B1950 (FK4) or J2000 (FK5), for example. In practice,
LST is used more loosely to mean either LMST or "Local Apparent Sidereal
Time" = GAST + (equation of the equinoxes). The operational definition
probably varies from one observatory to the next.